TY - JOUR TI - An SDRE-Based Approach for HIV Feedback Control and Control of Thin Film Growth in a CVD Reactor AU - Banks, H.T. AU - Beeler, S.C. AU - Kwon, Hee-Dae AU - Lewis, B.M. AU - Toivanen, J.A. AU - Tran, H.T. T2 - IFAC Proceedings Volumes AB - A number of computational methodologies have been proposed in the literature to design and synthesize feedback controls when the plant is modeled by nonlinear dynamical systems. One of the highly promising and rapidly emerging methodologies for designing nonlinear controllers is the state-dependent Riccati equation (SDRE) method in the context of the nonlinear regulator problem. In essence, SDRE mimics the linear quadratic regulator theory by using direct parametrization to rewrite the nonlinear state function as a product of a state-dependent coefficient matrix with the state vector. This paper presents an overview of our successful effort on the application of SDRE for the regulation of the growth of thin films in a high pressure chemical vapor deposition (CVD) and for the development of optimal dynamic multi-drug therapies for human immunodeficiency virus (HIV) infection. DA - 2011/1// PY - 2011/1// DO - 10.3182/20110828-6-it-1002.03412 VL - 44 IS - 1 SP - 9601-9606 J2 - IFAC Proceedings Volumes LA - en OP - SN - 1474-6670 UR - http://dx.doi.org/10.3182/20110828-6-it-1002.03412 DB - Crossref ER - TY - CHAP TI - Interfaces for the Helmholtz Equation with High Order Accuracy AU - Turkel, E. AU - Tsynkov, S. T2 - Proceedings of the 10th International Conference on Mathematical and Numerical Aspects of Wave Propagation, WAVES 2011, Vancouver, Canada, July 25--29, 2011 PY - 2011/// SP - 659-662 UR - https://stsynkov.math.ncsu.edu/publications/a66e_waves11.pdf ER - TY - JOUR TI - Patient specific modeling of cardiovascular and respiratory dynamics during hypercapnia AU - Ellwein, L M AU - Pope, S R AU - Xie, A AU - Batzel, J AU - Kelley, C T AU - Olufsen, M S T2 - Mathematical Biosciences DA - 2011/// PY - 2011/// VL - 241 IS - 1 SP - 56--74 ER - TY - JOUR TI - Finding A Stable Solution of A System of Nonlinear Equations AU - Kelley, C T AU - Qi, L AU - Tong, X AU - Yin, H T2 - J. Indus. Manag. Opt. DA - 2011/// PY - 2011/// VL - 7 SP - 497-521 ER - TY - JOUR TI - Users' Guide for imfil AU - Kelley, C T DA - 2011/// PY - 2011/// ER - TY - CONF TI - Application of a Modified Nelder-Mead Algorithm for calibrating RF Analog Integrated Circuits AU - Wyers, E.J. AU - Steer, M.B. AU - Kelley, C.T. AU - Franzon, P.D. C2 - 2011/// C3 - Proceedings GOMACTech'11 DA - 2011/// SP - 545–548 ER - TY - BOOK TI - Implicit Filtering AU - Kelley, C T DA - 2011/// PY - 2011/// PB - SIAM ER - TY - JOUR TI - Nonlinear Least Squares Problems and Subset Selection AU - Ipsen, I C F AU - Kelley, C T AU - Pope, S R T2 - SIAM J. Numer. Anal. DA - 2011/// PY - 2011/// VL - 49 SP - 1244-1266 ER - TY - ER - TY - CHAP TI - Central-upwind schemes for Boussinesq paradigm equations AU - Chertock, Alina AU - Christov, Christo I. AU - Kurganov, Alexander T2 - Computational science and high performance computing IV AB - We develop a new accurate and robust numerical method for the Boussinesq paradigm equation (BPE). To design the method we first introduce a change of variables, for which the BPE takes the form of a nonlinear wave equation with the global pressure, and rewrite the wave equation as a system of conservation laws with a global flux. We then apply a Godunov-type central-upwind scheme together with an efficient FFT-based elliptic solver to the resulting system. Making use of the new scheme, we investigate the propagation of one- and two-dimensional solitary waves of BPE and identify their solitonic behaviour. PY - 2011/// DO - 10.1007/978-3-642-17770-5_20 VL - 115 SP - 267-281 PB - Springer, Berlin UR - https://doi-org.prox.lib.ncsu.edu/10.1007/978-3-642-17770-5_20 ER - TY - JOUR TI - Application of Proper Orthogonal Decomposition (POD) to inverse problems in saturated groundwater flow AU - Winton, Corey AU - Pettway, Jackie AU - Kelley, C. T. AU - Howington, Stacy AU - Eslinger, Owen J. T2 - ADVANCES IN WATER RESOURCES AB - We develop a new Proper Orthogonal Decomposition (POD) reduced order model for saturated groundwater flow, and apply that model to an inverse problem for the hydraulic conductivity field. We use sensitivities as the POD basis. We compare the output when the optimizer uses the reduced order model against results obtained with a full PDE based model. The solutions generated using the POD reduced model are comparable in residual norm to the solutions formed using only the full-scale model. The material parameters are similarly comparable. The time to solution when using the reduced model is reduced by at least an order of magnitude, as are the number of calls to the full model. DA - 2011/12// PY - 2011/12// DO - 10.1016/j.advwatres.2011.09.007 VL - 34 IS - 12 SP - 1519-1526 SN - 1872-9657 KW - Proper Orthogonal Decomposition KW - Optimization KW - Parameter estimation KW - Inverse problem KW - Saturated groundwater flow ER - TY - JOUR TI - Receding Horizon Control of HIV AU - David, John AU - Tran, Hien AU - Banks, H. T. T2 - OPTIMAL CONTROL APPLICATIONS & METHODS AB - This paper describes a model of the immunologic response of the human immunodeficiency virus (HIV) in individuals. It then illustrates how a Receding Horizon Control (RHC) methodology can be used to drive the system to a stable equilibrium in which a strong immune response controls the viral load in the absence of drug treatment. We also illustrate how this feedback methodology can overcome unplanned treatment interruptions, inaccurate or incomplete data and imperfect model specification. We consider how ideas from stochastic estimation can be used in conjunction with RHC to create a robust treatment methodology. We then consider the performance of this methodology over random simulations of the previously considered clinical conditions. Copyright © 2010 John Wiley & Sons, Ltd. DA - 2011/// PY - 2011/// DO - 10.1002/oca.969 VL - 32 IS - 6 SP - 681-699 SN - 1099-1514 KW - HIV model KW - Receding Horizon Control KW - extended Kalman filter KW - state estimator ER - TY - JOUR TI - A new model for the estimation of cell proliferation dynamics using CFSE data AU - Banks, H. T. AU - Sutton, Karyn L. AU - Thompson, W. Clayton AU - Bocharov, Gennady AU - Doumic, Marie AU - Schenkel, Tim AU - Argilaguet, Jordi AU - Giest, Sandra AU - Peligero, Cristina AU - Meyerhans, Andreas T2 - JOURNAL OF IMMUNOLOGICAL METHODS AB - CFSE analysis of a proliferating cell population is a popular tool for the study of cell division and divisionlinked changes in cell behavior. Recently Banks et al. (2011), Luzyanina et al. (2009), Luzyanina et al. (2007), a partial differential equation (PDE) model to describe lymphocyte dynamics in a CFSE proliferation assay was proposed. We present a significant revision of this model which improves the physiological understanding of several parameters. Namely, the parameter used previously as a heuristic explanation for the dilution of CFSE dye by cell division is replaced with a more physical component, cellular autofluorescence. The rate at which label decays is also quantified using a Gompertz decay process. We then demonstrate a revised method of fitting the model to the commonly used histogram representation of the data. It is shown that these improvements result in a model with a strong physiological basis which is fully capable of replicating the behavior observed in the data. DA - 2011/10/28/ PY - 2011/10/28/ DO - 10.1016/j.jim.2011.08.014 VL - 373 IS - 1-2 SP - 143-160 SN - 1872-7905 KW - Cell proliferation KW - Cell division number KW - CFSE KW - Label structured population dynamics KW - Partial differential equations KW - Inverse problems ER - TY - JOUR TI - Host immune responses that promote initial HIV spread AU - Wendelsdorf, K. AU - Dean, G. AU - Hu, Shuhua AU - Nordone, S. AU - Banks, H. T. T2 - JOURNAL OF THEORETICAL BIOLOGY AB - The host inflammatory response to HIV invasion is a necessary component of the innate antiviral activity that vaccines and early interventions seek to exploit/enhance. However, the response is dependent on CD4+ T-helper cell 1 (Th1) recruitment and activation. It is this very recruitment of HIV-susceptible target cells that is associated with the initial viral proliferation. Hence, global enhancement of the inflammatory response by T-cells and dendritic cells will likely feed viral propagation. Mucosal entry sites contain inherent pathways, in the form of natural regulatory T-cells (nTreg), that globally dampen the inflammatory response. We created a model of this inflammatory response to virus as well as inherent nTreg-mediated regulation of Th1 recruitment and activation. With simulations using this model we sought to address the net effect of nTreg activation and its specific functions as well as identify mechanisms of the natural inflammatory response that are best targeted to inhibit viral spread without compromising initial antiviral activity. Simulation results provide multiple insights that are relevant to developing intervention strategies that seek to exploit natural immune processes: (i) induction of the regulatory response through nTreg activation expedites viral proliferation due to viral production by nTreg itself and not to reduced Natural Killer (NK) cell activity; (ii) at the same time, induction of the inflammation response through either DC activation or Th1 activation expedites viral proliferation; (iii) within the inflammatory pathway, the NK response is an effective controller of viral proliferation while DC-mediated stimulation of T-cells is a significant driver of viral proliferation; and (iv) nTreg-mediated DC deactivation plays a significant role in slowing viral proliferation by inhibiting T-cell stimulation, making this function an aide to the antiviral immune response. DA - 2011/11/21/ PY - 2011/11/21/ DO - 10.1016/j.jtbi.2011.08.012 VL - 289 SP - 17-35 SN - 1095-8541 KW - HIV KW - Innate inflammatory response pathway KW - Regulatory response pathway KW - Mathematical model ER - TY - JOUR TI - Parameter estimation for the heat equation on perforated domains AU - Banks, H. T. AU - Cioranescu, D. AU - Criner, A. K. AU - Winfree, W. P. T2 - Journal of Inverse and Ill-Posed Problems DA - 2011/// PY - 2011/// VL - 19 IS - 6 SP - 825-857 ER - TY - JOUR TI - Numerical Study of Surfactant-Laden Drop-Drop Interactions AU - Xu, Jian-Jun AU - Li, Zhilin AU - Lowengrub, John AU - Zhao, Hongkai T2 - COMMUNICATIONS IN COMPUTATIONAL PHYSICS AB - Abstract In this paper, we numerically investigate the effects of surfactant on drop-drop interactions in a 2D shear flow using a coupled level-set and immersed interface approach proposed in (Xu et al., J. Comput. Phys., 212 (2006), 590-616). We find that surfactant plays a critical and nontrivial role in drop-drop interactions. In particular, we find that the minimum distance between the drops is a non-monotone function of the surfactant coverage and Capillary number. This non-monotonic behavior, which does not occur for clean drops, is found to be due to the presence of Marangoni forces along the drop interfaces. This suggests that there are non-monotonic conditions for coalescence of surfactant-laden drops, as observed in recent experiments of Leal and co-workers. Although our study is two-dimensional, we believe that drop-drop interactions in three-dimensional flows should be qualitatively similar as the Maragoni forces in the near contact region in 3D should have a similar effect. DA - 2011/8// PY - 2011/8// DO - 10.4208/cicp.090310.020610a VL - 10 IS - 2 SP - 453-473 SN - 1991-7120 KW - Surfactants KW - drops KW - coalescence KW - surface tension KW - Marangoni effect KW - level-set method KW - immersed interface method KW - Stokes flow ER - TY - JOUR TI - Dynamic evasion-interrogation games with uncertainty in the context of electromagetics AU - Banks, H. T. AU - Hu, S. H. AU - Ito, K. AU - Muccio, S. G. T2 - Numerical Mathematics: Theory, Methods and Applications DA - 2011/// PY - 2011/// VL - 4 IS - 3 SP - 359-378 ER - TY - JOUR TI - Statistical Parameter Estimation for Macro Fiber Composite Actuators using the Homogenized Energy Model AU - Hu, Zhengzheng AU - Smith, Ralph C. AU - Stuebner, Michael AU - Hays, Michael AU - Oates, William S. T2 - BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2011 AB - Macro Fiber Composites (MFC) are planar actuators comprised of PZT fibers embedded in an epoxy matrix that is sandwiched between electrodes. Due to their construction, they exhibit significant durability and flexibility in addition to being lightweight and providing broadband inputs. They are presently being considered for a range of applications including positioning and control of membrane mirrors and configurable aerospace structures. However, they also exhibit hysteresis and constitutive nonlinearities that must be incorporated in models to achieve the full potential of the devices. In this paper, we discuss the development of a model that quantifies the hysteresis and constitutive nonlinearities in a manner that promotes subsequent control design. The constitutive model is constructed using the homogenized energy framework for ferroelectric hysteresis and used to develop resulting system models. The performance of the models is validated with experimental data. DA - 2011/// PY - 2011/// DO - 10.1117/12.884622 VL - 7978 SP - SN - 0277-786X KW - Nonlinear piezoelectric model KW - macro fiber composite ER - TY - JOUR TI - Quasi-Lacunae of Maxwell's Equations AU - Petropavlovsky, S. V. AU - Tsynkov, S. V. T2 - SIAM Journal on Applied Mathematics AB - Classical lacunae in the solutions of hyperbolic differential equations and systems (in the spaces of odd dimension) are a manifestation of the Huygens' principle. If the source terms are compactly supported in space and time, then, at any finite location in space, the solution becomes identically zero after a finite interval of time. In other words, the propagating waves have sharp aft fronts. For Maxwell's equations though, even if the currents that drive the field are compactly supported in time, they may still lead to the accumulation of charges. In that case, the solution won't have the lacunae per se. We show, however, that the notion of classical lacunae can be generalized, and that even when the steady-state charges are present, the waves still have sharp aft fronts. Yet behind those aft fronts, there is a nonzero electrostatic solution rather than one identically zero. DA - 2011/1// PY - 2011/1// DO - 10.1137/100798041 VL - 71 IS - 4 SP - 1109-1122 J2 - SIAM J. Appl. Math. LA - en OP - SN - 0036-1399 1095-712X UR - http://dx.doi.org/10.1137/100798041 DB - Crossref KW - waves propagation KW - unsteadiness KW - Huygens' principle KW - odd-dimension spaces KW - aft fronts KW - accumulation of charge KW - electrostatic solution ER - TY - JOUR TI - Adaptive Control Design for Hysteretic Smart Systems AU - McMahan, Jerry A. AU - Smith, Ralph C. T2 - BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2011 AB - Ferroelectric and ferromagnetic actuators are being considered for a range of industrial, aerospace, aeronautic and biomedical applications due to their unique transduction capabilities. However, they also exhibit hysteretic and nonlinear behavior that must be accommodated in models and control designs. If uncompensated, these effects can yield reduced system performance and, in the worst case, can produce unpredictable behavior of the control system. In this paper, we address the development of adaptive control designs for hysteretic systems. We review an MRAC-like adaptive control algorithm used to track a reference trajectory while computing online estimates for certain model parameters. This method is incorporated in a composite control algorithm to improve the tracking capabilities of the system. Issues arising in the implementation of these algorithms are addressed, and a numerical example is presented, comparing the results of each method. DA - 2011/// PY - 2011/// DO - 10.1117/12.884621 VL - 7978 SP - SN - 1996-756X KW - smart systems KW - hysteresis KW - adaptive control KW - composite control ER - TY - JOUR TI - Performance of Skart: A Skewness- and Autoregression-Adjusted Batch Means Procedure for Simulation Analysis AU - Tafazzoli, Ali AU - Wilson, James R. AU - Lada, Emily K. AU - Steiger, Natalie M. T2 - INFORMS JOURNAL ON COMPUTING AB - An analysis is given for an extensive experimental performance evaluation of Skart, an automated sequential batch means procedure for constructing an asymptotically valid confidence interval (CI) on the steady-state mean of a simulation output process. Skart is designed to deliver a CI satisfying user-specified requirements on absolute or relative precision as well as coverage probability. Skart exploits separate adjustments to the half-length of the classical batch means CI so as to account for the effects on the distribution of the underlying Student's t-statistic that arise from skewness (nonnormality) and autocorrelation of the batch means. Skart also delivers a point estimator for the steady-state mean that is approximately free of initialization bias. In an experimental performance evaluation involving a wide range of test processes, Skart compared favorably with other steady-state simulation analysis methods—namely, its predecessors ASAP3, WASSP, and SBatch, as well as ABATCH, LBATCH, the Heidelberger–Welch procedure, and the Law–Carson procedure. Specifically, Skart exhibited competitive sampling efficiency and closer conformance to the given CI coverage probabilities than the other procedures, especially in the most difficult test processes. DA - 2011/// PY - 2011/// DO - 10.1287/ijoc.1100.0401 VL - 23 IS - 2 SP - 297-314 SN - 1526-5528 KW - simulation KW - statistical analysis KW - steady-state analysis KW - method of batch means KW - Cornish-Fisher expansion KW - autoregressive representation ER - TY - JOUR TI - RANK-DEFICIENT NONLINEAR LEAST SQUARES PROBLEMS AND SUBSET SELECTION AU - Ipsen, I. C. F. AU - Kelley, C. T. AU - Pope, S. R. T2 - SIAM JOURNAL ON NUMERICAL ANALYSIS AB - We examine the local convergence of the Levenberg–Marquardt method for the solution of nonlinear least squares problems that are rank-deficient and have nonzero residual. We show that replacing the Jacobian by a truncated singular value decomposition can be numerically unstable. We recommend instead the use of subset selection. We corroborate our recommendations by perturbation analyses and numerical experiments. DA - 2011/// PY - 2011/// DO - 10.1137/090780882 VL - 49 IS - 3 SP - 1244-1266 SN - 0036-1429 KW - nonlinear least squares KW - Levenberg-Marquardt algorithm KW - subset selection KW - singular value decomposition ER - TY - JOUR TI - A Brief Review of Elasticity and Viscoelasticity for Solids AU - Banks, Harvey Thomas AU - Hu, Shuhua AU - Kenz, Zackary R. T2 - ADVANCES IN APPLIED MATHEMATICS AND MECHANICS AB - Abstract There are a number of interesting applications where modeling elastic and/or viscoelastic materials is fundamental, including uses in civil engineering, the food industry, land mine detection and ultrasonic imaging. Here we provide an overview of the subject for both elastic and viscoelastic materials in order to understand the behavior of these materials. We begin with a brief introduction of some basic terminology and relationships in continuum mechanics, and a review of equations of motion in a continuum in both Lagrangian and Eulerian forms. To complete the set of equations, we then proceed to present and discuss a number of specific forms for the constitutive relationships between stress and strain proposed in the literature for both elastic and viscoelastic materials. In addition, we discuss some applications for these constitutive equations. Finally, we give a computational example describing the motion of soil experiencing dynamic loading by incorporating a specific form of constitutive equation into the equation of motion. DA - 2011/2// PY - 2011/2// DO - 10.4208/aamm.10-m1030 VL - 3 IS - 1 SP - 1-51 SN - 2075-1354 KW - Mathematical modeling KW - Eulerian and Lagrangian formulations in continuum mechanics KW - elasticity KW - viscoelasticity KW - computational simulations in soil KW - constitutive relationships ER - TY - JOUR TI - FINDING A STABLE SOLUTION OF A SYSTEM OF NONLINEAR EQUATIONS ARISING FROM DYNAMIC SYSTEMS AU - Kelley, Carl T. AU - Qi, Liqun AU - Tong, Xiaojiao AU - Yin, Hongxia T2 - JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION AB - In this paper, we present a new approach for finding a stablesolution of a system of nonlinear equations arising from dynamicalsystems. We introduce the concept ofstability functions and use this idea to constructstability solution models of severaltypical small signal stability problems in dynamical systems.Each model consists of a system of constrainedsemismooth equations. The advantage of the new models is twofold.Firstly, the stability requirement of dynamical systems iscontrolled by nonlinear inequalities. Secondly, the semismoothnessproperty of the stability functions makes the models solvable byefficient numerical methods. We introduce smoothing functions forthe stability functions and present a smoothing Newton methodfor solving the problems. Global and local quadratic convergence ofthe algorithm is established. Numerical examples from dynamicalsystems are also given to illustrate the efficiency of the newapproach. DA - 2011/5// PY - 2011/5// DO - 10.3934/jimo.2011.7.497 VL - 7 IS - 2 SP - 497-521 SN - 1553-166X KW - System of nonlinear equations KW - stable solutions KW - saddle-node bifurcation KW - Hopf bifurcation KW - stability functions KW - smoothing Newton method ER - TY - JOUR TI - Comparison of optimal design methods in inverse problems AU - Banks, H T AU - Holm, K AU - Kappel, F T2 - Inverse Problems AB - Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher Information Matrix (FIM). A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criteria with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model [13], the standard harmonic oscillator model [13] and a popular glucose regulation model [16, 19, 29]. DA - 2011/6/3/ PY - 2011/6/3/ DO - 10.1088/0266-5611/27/7/075002 VL - 27 IS - 7 SP - 075002 J2 - Inverse Problems OP - SN - 0266-5611 1361-6420 UR - http://dx.doi.org/10.1088/0266-5611/27/7/075002 DB - Crossref ER - TY - JOUR TI - The IIM in polar coordinates and its application to electro capacitance tomography problems AU - Ruiz Alvarez, Juan AU - Chen, Jinru AU - Li, Zhilin T2 - NUMERICAL ALGORITHMS DA - 2011/7// PY - 2011/7// DO - 10.1007/s11075-010-9436-3 VL - 57 IS - 3 SP - 405-423 SN - 1572-9265 KW - Immersed interface method KW - Polar coordinates KW - Interface KW - Discontinuous coefficients KW - Finite difference method KW - Electro capacitance tomography KW - Forward problem ER - TY - JOUR TI - Numerical Simulation of Time-Harmonic Waves in Inhomogeneous Media using Compact High Order Schemes AU - Britt, Steven AU - Tsynkov, Semyon AU - Turkel, Eli T2 - Communications in Computational Physics AB - Abstract In many problems, one wishes to solve the Helmholtz equation with variable coefficients within the Laplacian-like term and use a high order accurate method (e.g., fourth order accurate) to alleviate the points-per-wavelength constraint by reducing the dispersion errors. The variation of coefficients in the equation may be due to an inhomogeneous medium and/or non-Cartesian coordinates. This renders existing fourth order finite difference methods inapplicable. We develop a new compact scheme that is provably fourth order accurate even for these problems. We present numerical results that corroborate the fourth order convergence rate for several model problems. DA - 2011/3// PY - 2011/3// DO - 10.4208/cicp.091209.080410s VL - 9 IS - 3 SP - 520-541 J2 - Commun. comput. phys. LA - en OP - SN - 1815-2406 1991-7120 UR - http://dx.doi.org/10.4208/cicp.091209.080410s DB - Crossref KW - Helmholtz equation KW - variable coefficients KW - high order accuracy KW - compact finite differences ER - TY - JOUR TI - High order compact finite difference schemes for the helmholtz equation with discontinuous coefficients AU - Feng, X. F. AU - Li, Z. L. AU - Qiao, Z. H. T2 - Journal of Computational Mathematics DA - 2011/// PY - 2011/// VL - 29 IS - 3 SP - 324-340 ER - TY - JOUR TI - Dual Carrier Probing for Spaceborne SAR Imaging AU - Smith, E. M. AU - Tsynkov, S. V. T2 - SIAM Journal on Imaging Sciences AB - Spaceborne imaging of the Earth's surface by synthetic aperture radar (SAR) may be adversely affected by the ionosphere that causes distortions of the signals emitted and received by the radar antenna. In our previous publication on the subject [SIAM J. Imaging Sci., 2 (2009) pp. 140–182], we have analyzed those distortions for the inhomogeneous ionosphere described by the cold plasma model. Based on the analysis, we have concluded that the deterioration of SAR images was due to the mismatch between certain parameters of the actual received signal, which is slowed down by the temporal dispersion in the ionosphere, and the corresponding parameters of the matched filter, which is taken as if the propagation were unobstructed. Consequently, to improve the quality of the images, the filter must be corrected. However, to get the appropriate correction, one needs to know some key characteristics of the ionosphere precisely at the time and place the image is taken. To obtain those characteristics, we currently propose probing the terrain, and hence the ionosphere, on two distinct carrier frequencies. We also investigate the performance of the matched filters that were corrected this way and show that the final quality of the images, i.e., their resolution and sharpness evaluated using the SAR ambiguity theory, indeed improves. DA - 2011/1// PY - 2011/1// DO - 10.1137/10078325x VL - 4 IS - 2 SP - 501-542 J2 - SIAM J. Imaging Sci. LA - en OP - SN - 1936-4954 UR - http://dx.doi.org/10.1137/10078325X DB - Crossref KW - synthetic aperture radar KW - Earth's ionosphere KW - dispersion of radio waves KW - image distortions KW - cold plasma KW - matched filter KW - multicarrier probing KW - correction of the filter KW - range and azimuthal resolution KW - image sharpness ER - TY - JOUR TI - An energy regularization for cauchy problems of laplace equation in annulus domain AU - Han, H. AU - Ling, L. AU - Takeuchi, T. T2 - Communications in Computational Physics DA - 2011/// PY - 2011/// VL - 9 IS - 4 SP - 878-896 ER - TY - JOUR TI - Adaptive mesh refinement for elliptic interface problems using the non-conforming immersed finite element method AU - Wu, C. T. AU - Li, Z. L. AU - Lai, M. C. T2 - International Journal of Numerical Analysis and Modeling DA - 2011/// PY - 2011/// VL - 8 IS - 3 SP - 466-483 ER - TY - JOUR TI - A DETERMINISTIC METHODOLOGY FOR ESTIMATION OF PARAMETERS IN DYNAMIC MARKOV CHAIN MODELS AU - Ortiz, A. R. AU - Banks, H. T. AU - Castillo-Chavez, C. AU - Chowell, G. AU - Wang, X. T2 - JOURNAL OF BIOLOGICAL SYSTEMS AB - A method for estimating parameters in dynamic stochastic (Markov Chain) models based on Kurtz's limit theory coupled with inverse problem methods developed for deterministic dynamical systems is proposed and illustrated in the context of disease dynamics. This methodology relies on finding an approximate large-population behavior of an appropriate scaled stochastic system. The approach leads to a deterministic approximation obtained as solutions of rate equations (ordinary differential equations) in terms of the large sample size average over sample paths or trajectories (limits of pure jump Markov processes). Using the resulting deterministic model, we select parameter subset combinations that can be estimated using an ordinary-least-squares (OLS) or generalized-least-squares (GLS) inverse problem formulation with a given data set. The selection is based on two criteria of the sensitivity matrix: the degree of sensitivity measured in the form of its condition number and the degree of uncertainty measured in the form of its parameter selection score. We illustrate the ideas with a stochastic model for the transmission of vancomycin-resistant enterococcus (VRE) in hospitals and VRE surveillance data from an oncology unit. DA - 2011/3// PY - 2011/3// DO - 10.1142/s0218339011003798 VL - 19 IS - 1 SP - 71-100 SN - 1793-6470 KW - Markov Chain Stochastic Models KW - Inverse Problems KW - Parameter Estimation KW - Parameter Selection KW - Large Population Sample Path Approximations ER - TY - JOUR TI - Efficient Parallel Computation of Molecular Potential Energy Surfaces for the Study of Light-Induced Transition Dynamics in Multiple Coordinates AU - Mokrauer, David AU - Kelley, C. T. AU - Bykhovski, Alexei T2 - IEEE TRANSACTIONS ON NANOTECHNOLOGY AB - The conformational dynamics of molecules that arise due to light-induced transitions are critically important in many biochemical reactions, and therefore dictate the functionality of many types of biological sensors. Therefore, researchers of biological science and biological-inspired technology often need to prescribe the molecular geometry of the stable states and the associated transition trajectories that occur as a result of external excitation, e.g., light-induced transitions from the ground state to the excited states. The traditional approach to study this type of phenomenology is to limit the number of varying molecular coordinates to one or a few due to the considerable computational expense of the required physically modeling required for generating an accurate physical model for analysis. While the conformational dynamics for some types of simple molecules (e.g., retinal) are known to be adequately described by one or few numbers of molecular coordinates, light-induced transitions in arbitrarily complex molecules can be expected to involve the influence of multiple coordinates, and their influence can be expected to vary as a function of time. The research reported here will address the development of parallel computational algorithms that allow for the highly efficient study of molecular conformational dynamics over multiple numbers of multidimensional energy surfaces. Here, the goal is the development of a simulation tool that is capable of: constructing physically accurate multidimensional potential energy surfaces (i.e., from first-principle physical modeling codes); deriving the natural trajectories to local minima within individual surfaces; and that allows for dynamics human interfacing for specifying the transition between energy surfaces and the number of coordinates to be used for the optimization within a particular energy surface. As will be illustrated, this type of physics-based simulation tool will allow researchers to efficiently explore the light-induced conformation dynamics associated with complex biomolecules, and therefore, be a useful tool for the design of biological-sensing processes in the future. DA - 2011/1// PY - 2011/1// DO - 10.1109/tnano.2010.2058862 VL - 10 IS - 1 SP - 70-74 SN - 1941-0085 KW - Algorithm design and analysis KW - chemical sensors KW - 1H NMR KW - nanoelectonics KW - stibenes KW - UV-vis spectroscopy ER - TY - JOUR TI - Discretized Tikhonov regularization by reproducing kernel Hilbert space for backward heat conduction problem AU - Hon, Y. C. AU - Takeuchi, T. T2 - Advances in Computational Mathematics DA - 2011/// PY - 2011/// VL - 34 IS - 2 SP - 167-183 ER - TY - JOUR TI - A finite element method for elasticity interface problems with locally modified triangulations AU - Xie, H. AU - Li, Z. L. AU - Qiao, Z. H. T2 - International Journal of Numerical Analysis and Modeling DA - 2011/// PY - 2011/// VL - 8 IS - 2 SP - 189-200 ER - TY - JOUR TI - Estimation of Cell Proliferation Dynamics Using CFSE Data AU - Banks, H. T. AU - Sutton, Karyn L. AU - Thompson, W. Clayton AU - Bocharov, Gennady AU - Roose, Dirk AU - Schenkel, Tim AU - Meyerhans, Andreas T2 - BULLETIN OF MATHEMATICAL BIOLOGY AB - Advances in fluorescent labeling of cells as measured by flow cytometry have allowed for quantitative studies of proliferating populations of cells. The investigations (Luzyanina et al. in J. Math. Biol. 54:57–89, 2007; J. Math. Biol., 2009; Theor. Biol. Med. Model. 4:1–26, 2007) contain a mathematical model with fluorescence intensity as a structure variable to describe the evolution in time of proliferating cells labeled by carboxyfluorescein succinimidyl ester (CFSE). Here, this model and several extensions/modifications are discussed. Suggestions for improvements are presented and analyzed with respect to statistical significance for better agreement between model solutions and experimental data. These investigations suggest that the new decay/label loss and time dependent effective proliferation and death rates do indeed provide improved fits of the model to data. Statistical models for the observed variability/noise in the data are discussed with implications for uncertainty quantification. The resulting new cell dynamics model should prove useful in proliferation assay tracking and modeling, with numerous applications in the biomedical sciences. DA - 2011/1// PY - 2011/1// DO - 10.1007/s11538-010-9524-5 VL - 73 IS - 1 SP - 116-150 SN - 1522-9602 KW - Cell proliferation KW - CFSE KW - Label structured population dynamics KW - Partial differential equations KW - Inverse problems ER -